Solve for $x$ and $y$ using elimination. ${-x-4y = -19}$ ${-x-5y = -22}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${x+4y = 19}$ $-x-5y = -22$ Add the top and bottom equations together. $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-x-4y = -19}\thinspace$ to find $x$ ${-x - 4}{(3)}{= -19}$ $-x-12 = -19$ $-x-12{+12} = -19{+12}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 3}$ into $\thinspace {-x-5y = -22}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(3)}{= -22}$ ${x = 7}$